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دوره‌ها ماژول‌ها مجموعه‌داده‌ها منابع مدرس

آزمایشگاه داده‌های رسمی

منابع داده عمومی برای مثال‌ها، نمودارها و تمرین‌های R

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درس 8 از 16

Independent and Dependent Events

خانه/ماژول‌ها/ماژول 5/Independent and Dependent Events

Evaluate independence through conditional and multiplication checks without causal overreach.

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42 دقیقه50% مسیر

هدف‌های یادگیریتا پایان این درس، دانشجویان می‌توانند:

1Define the events and probability quantities used in independent and dependent events.
2Select and calculate an appropriate probability rule with a visible denominator or assumption.
3Interpret the result for a business decision without overstating certainty or causation.

Theory

Core probability reasoning

Evaluate independence through conditional and multiplication checks without causal overreach.

توضیح 1

Independent: Knowing B does not change the probability of A.

توضیح 2

Dependent: The conditional probability differs from the marginal.

توضیح 3

Causation: A stronger claim requiring design and mechanism evidence.

اصطلاحات

Concept map

Independent

Knowing B does not change the probability of A.

P(A given B)=P(A).

Dependent

The conditional probability differs from the marginal.

Membership is associated with receipt choice.

Causation

A stronger claim requiring design and mechanism evidence.

Not established by dependence alone.

نمادگذاری و فرمول‌ها

Independence checks

رابطه اصلی

P(A given B) = P(A), or P(A and B) = P(A)P(B)

Define every event before substituting values, then validate the result and denominator.

گام 1Calculate both sides with consistent events.
گام 2Compare exactly or describe practical differences.
گام 3Avoid a causal conclusion.

فعالیت تعاملی

independence checker

P(A)P(B)P(A and B)

Joint minus product

0

0.3 - 0.3

The stated values are consistent with independence. This comparison does not establish causation.

مثال حل‌شده

Receipt choice

سناریو

Digital-receipt use differs between loyalty and non-loyalty orders.

Dependence can reflect selection or another variable rather than a direct effect.

ارتباط با R

R note: Independence Checks

Run and edit the code, inspect intermediate output, and use the movable R Code Guide while practising.

Live R Lab

Independence Checks

Compare conditional and marginal probabilities without turning association into causation.

Editable R code

Results

Ready to run

Ready to run

Ready to run. Results, errors, tables, plots, and fallback messages will appear here.

Compare conditional and marginal probability.

Compare joint with product.

State the descriptive limit.

Dataset provenance

Original synthetic data generated for STATLAB Academy. No textbook data used.

Interpretation safeguard

Independence is an assumption or empirical property, not a casual default.

بازاندیشی

مکث و یادداشت

Where could an unclear event definition or assumption change the conclusion in independent and dependent events?

Name the event, denominator, probability interpretation, and one operational limitation.

دستیار

Ask your probability coach

Help me reason through Independent and Dependent Events by asking questions about my event definitions, denominator, formula choice, assumptions, and interpretation. Do not give a quiz answer before I submit.

ارزیابی پایانی

Lesson checkpoint

Use a hint before submitting if needed. Full calculations and interpretations appear after submission.

Checkpoint

Module 5 Lesson 8 Checkpoint

Question 1 of 2. Answered 0/2. Passing score: 70%.

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Question 1: True or false

easyCalculate and responsibly interpret probability for a defined event.

P(A)=0.6, P(B)=0.5, and P(A and B)=0.30. These values are consistent with independence.

FalseTrue

منبع

Recommended reading

Explore additional probability explanations and exercises from properly licensed or publisher resources.

منبع

Module 5 learning material

Download an original worksheet or guide for this lesson.

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